Method of digitally squaring the ratio of two frequencies

ABSTRACT

This invention relates to a method of digitally squaring the ratio of two frequencies as for example in the measurement of weight by a chord balance. As distinct from prior art methods utilizing three counters the present invention utilizes only two counters and includes a flip-flop and a gate circuit for additive and subtractive counting.

United States Patent [1 1 [111 3,821,536 Berg June 28, 1974 [5 METHOD OFDIGITALLY SQUARING THE 2,951,986 9/1960 Gordon 235/1503 x 3,040,9836/1962 Bigelow RATIO OF W FREQUENCIES 3,588,473 6/1971 Meyer 235/92 F0Inventor: ist p g, Gottmgen, 3,662,159 5/1972 Schief 235/92 FQ Germany[73] Assignee: Sartorius-Werke GmbH, Gottingen, I

Germany Primary Examiner-Malcolm A. Morrison Assistant Examiner-James F.Gottman [22] Flled: Sept- 13, 1972 Attorney, Agent, or FirmEdmund M.Jaskiewicz [2!] App]. No.: 288,556

[30] Foreign Application Priority Data Sept. 28, 1971 Germany 2148323[57] ABSTRACT 52 5 CL n 235 1 0, 235/1503 235 92 This invention relatesto a method of digitally squaring 324/73 D the ratio of two frequenciesas for example in the mea- 51 int. Cl. G06f 7/39 suremem of weight y achord balance As distinct [58] Field Of Search 235/160, 150.3, 92 F0,from Prior art methods utilizing three counters the 235 92 CC, 92 p 92DM, 92 T; 324/73 D present invention utilizes only two counters andincludes a flip-flop and a gate circuit for additive and 5 ReferencesCited subtractive counting.

UNITED STATES PATENTS 2,951,202 8/1960 Gordon 324/78 D 10 Claims, 1Drawing Figure D A A )r 9 F F o I I M F 0 i 1 5 T A 0 tr t METHOD OFDIGITALLY SQUARING THE RATIO OF TWO FREQUENCIES The present inventionrelates to a method of digitally squaring the ratio of two frequencies.

The requirement of squaring the ratio of two frequencies arises forexample in a balance in which a chord is stressed by the combined actionof a constant initial stressing force V and a weight G to be measured.The natural frequency of the cord f,, is proportional to the square rootof the total load:

where a is a constant.

A second chord is stressed only by the initial stressing force V so thatits natural frequency is given by the equation:

again where a is a constant.

The weight G to be measured may then be calculated by dividing the twoabove equations as set out below:

fl/f2 V +G)/ V,

from which G V [m /I 1 It will be understood that the ratio ffi/f, mustbe determined before G, the weight to be measured, can be calculated.

Methods of digitally squaring which use three counters are known. By wayof example, a first counter having forward and backward inputs, countsthe difference between the frequencies f, and f during a period T, whichis determined by a second counter which counts f, up to a preset numberof oscillations N,.

T, is followed by a time interval T during which the reading Z, of thefirst counter is returned to 0 by the frequency f,

Finally a third counter measures the frequency f, during the timeintervals T, and T its reading 2,, then indicating the total number ofpulses.

Hence Thus, three counters are required. Furthermore, the first counterhas to have forward and backward inputs which can be usedsimultaneously. This requires heavy expenditure on circuitry, so thatcoincident pulses can also be correctly counted at the inputs.

An aspect of the invention is to simplify the abovementioned procedureand in which only two counters are required.

According to the present invention there is provided a method ofdigitally squaring the ratio of two frequencies which comprises feedingpulses at the second frequency to a first counter for a first timeperiod through a gate circuit with a control element switched into onestable state, feeding pulses at the first frequency to a second counterin an additive state, the first counter being such that after a presetnumber of pulses have been counted the counter reaches a zero setting,an output signal being arranged to switch the control element into asecond stable state to terminate the first time period and to commence asecond time period during which the second counter is switched to asubtractive state by the control element and receives pulses at thesecond frequency through the gate circuit whilst the first counter addspulses of the first frequency for the second time period, the gatecircuit being closed when a zerosetting is attained on the secondcounter so that the digitally squared reading is obtained on the firstcounter.

An additional advantage of the method in accordance with the inventionis that forward-backward counting is separated with respect to time.

The invention will now be described further by way of example withreference to the accompanying drawing the single FIGURE of whichillustrates a circuit diagram suitable for carrying out the method ofthe invention.

The circuit includes two counters A and B, a gate circuit embodying sixgates designated 1 to 6 and a bistable flip-flop FF which controls thegate circuit and the change-over of counter B from addition tosubtraction. l, 2, 4, 5 and 8 are AND gates, 3, 6 and 7 are OR gates and9 is an inverter.

A starting pulse applied through AND gate 8 switches the flip-flop FFinto one stable state corresponding with addition and sets the presetnumber of oscillations N in the counter A (-N corresponds to 10' N, nbeing the number of decades in the counter). The Counter B is set tozero.

Counter B is switched to addition by the flip-flop FF and the gates land 5 are opened, so that counter B receives pulses of frequency f,which are fed to one input and counter A receives pulses of frequency f,which are fed to the second input. After N pulses have been counted incounter A, i.e., after the period T N/f counter A reaches a zero readingand produces a signal which switches the flip-flop FF into its otherstable state corresponding with subtraction. At this stage counter B hascounted Z T f, pulses. When in the state corresponding with, subtractionflip-flop FF switches counter B to subtraction, closes the gates l and 5and opens the gates 2 and 4, since the counter B simultaneously producesa signal 2,, 0. If f, is equal to 0, i.e. Z 0, all the gates remainclosed and the result (fi/f, O can be read from the counter A. In thenormal case where f, a 0, a new counting period T commences during whichpulses of frequency f, are subtracted from the counter reading 2,, incounter B, and pulses of the frequency f, are added up commencing from 0in the counter A. The counting period T terminates when counter Breaches a zero reading.

Hence:

A result 2,, T f, N(f,/f,) is present in the counter A and remains incounter A until the commencement of a fresh cycle. The counter B readszero and is thus in a correct state for a following measuring operation.

A fresh cycle commences when a starting pulse sets the reading of thecounter A to N and sets the flip-flop FF into a state corresponding toaddition again. The result can be read from counter A between two cyclesand, if required, can be further processed. A signal is present atoutput D during the period T and T and prevents a reading from beingtaken from the counter A by way of known circuits not illustrated in theFIG- URE.

If an additional additive constant K is required for the evaluation, thecounter A is set to N K during starting and the output is switched insuch a manner that a signal is supplied to flip-flop FF when the counterreading is K. The counter A is then at K at the commencement of themeasuring time T and, at the end of T indicates:

K may be positive or negative.

In the case of a chord balance, the input of this constant K can servefor the digital suppression of a tare weight.

lf the measurement time is not synchronized with the pulse train, anerror of ii counting steps occurs each time virtually uniform pulses arecounted. in the described circuit, the commencement of T is given by thestarting signal, the end of T and thus the beginning of T issynchronized with f and likewise the end of T Thus, with the exceptionof the triggering error, T is exactly equal to Z /f while T isdetermined only by T N i l/f Thus, with result Z,,, the error in theduration of the measuring interval T is added to the error of i lcounting steps as a result of the absence of synchronization of themeasuring interval T and the counting frequency f However, this error ofT can be eliminated by the starting signal becoming effective only whenan f pulse arrives. It does not matter whether this f pulse, which hasallowed the start to become effective, is added in or not, since thenumber N is optionally predetermined. The only important thing is thatthe circuit should be designed in such a manner that it always operatesin the same manner.

Referring again to the drawing, an RC coupling on the input side of thegate 8 indicates a time lag which ensures that counter A receives astarting signal after the synchronizing pulse, i.e., the counter A doesnot count in the synchronizing pulse. The time lag must be longer thanthe transmit time of the f2 pulse through the gates and 6, but shorterthan the minimum period of the frequency f The method of digitallysquaring the ratio of two frequencies described herein is intended to beillustrative only and it will be appreciated that variations andmodifications may be resorted to without departing from the spirit andscope of the invention as set forth in the attached claims.

I claim:

l. A method of digitally squaring the ratio of two frequencies usingcounters comprising the steps of feeding pulses at a second frequency toa first counter whose initial readinghas been set at-N for a first timeperiod which is equal to the N-fold duration of a cycle of the secondfrequency to bring the reading of the first counter to zero, feedingpulses for the first time period at a first frequency to a secondcounter whose initial reading has been set at zero such that the readingof the second counter is increased from zero, and in a second timeperiod which is equal to the time required to bring the reading of thesecond counter back to zero subtracting pulses at the second frequencyfrom the second counter and adding pulses at the first frequency to thefirst counter so that the digital reading shown on the first counterupon expiration of the first and second time periods is N times thedesired ratio of squared frequencies to which is added the initialreading of the first counter.

2. A method as claimed in claim 1 wherein the initial reading on thefirst counter is other than zero.

3. A process as claimed in claim 2 wherein said initial readingcorresponds to the tare weight to be overcome on a spring balance.

4. A method as claimed in claim 1 and the step of synchronizing thebeginning of the first time period with a reference frequency.

5. A method as claimed in claim 1 wherein the method is used for themeasurement of weight by a spring balance.

6. A method as set forth in claim 1 which additionally comprises thestep of presetting the first counter to a value including a constant Ksuch that the first counter supplies a pulse to the control element uponattaining the preset value including the constant K, whereby the totalof constant K and the measured value is available in said first counterat the end of the second time period.

7. A method as set forth in claim 6 wherein the constant K is positive.

8. A method as set forth in claim 1 wherein the comencement of saidfirst time period is synchronized to the second frequency.

9. An apparatus for digitally squaring the ratio of two frequenciescomprising first and second counters, gate circuit means for connectingsaid counters to sources of first and second frequencies and forconnecting said counters to each other, and a bistable switching elementresponsive to said first counter for reversing the direction of countingof said first and second counters and for interchanging through saidgate circuit means the frequency sources to said counters.

10. An apparatus as claimed in claim 9 wherein said gate circuit meanscomprises a gate element for blocking the resetting of the initialreading into the first counter prior to the expiration of the first andsecond time periods.

1. A method of digitally squaring the ratio of two frequencies usingcounters comprising the steps of feeding pulses at a second frequency toa first counter whose initial reading has been set at N for a first timeperiod which is equal to the N-fold duration of a cycle of the secondfrequency to bring the reading of the first counter to zero, feedingpulses for the first time period at a first frequency to a secondcounter whose initial reading has been set at zero such that the readingof the second counter is increased from zero, and in a second timeperiod which is equal to the time required to bring the reading of thesecond counter back to zero subtracting pulses at the second frequencyfrom the second counter and adding pulses at the first frequency to thefirst counter so that the digital reading shown on the first counterupon expiration of the first and second time periods is N times thedesired ratio of squared frequencies to which is added the initialreading of the first counter.
 2. A method as claimed in claim 1 whereinthe initial reading on the first counter is other than zero.
 3. Aprocess as claimed in claim 2 wherein said initial reading correspondsto the tare weight to be overcome on a spring balance.
 4. A method asclaimed in claim 1 and the step of synchronizing The beginning of thefirst time period with a reference frequency.
 5. A method as claimed inclaim 1 wherein the method is used for the measurement of weight by aspring balance.
 6. A method as set forth in claim 1 which additionallycomprises the step of presetting the first counter to a value includinga constant K such that the first counter supplies a pulse to the controlelement upon attaining the preset value including the constant K,whereby the total of constant K and the measured value is available insaid first counter at the end of the second time period.
 7. A method asset forth in claim 6 wherein the constant K is positive.
 8. A method asset forth in claim 1 wherein the comencement of said first time periodis synchronized to the second frequency.
 9. An apparatus for digitallysquaring the ratio of two frequencies comprising first and secondcounters, gate circuit means for connecting said counters to sources offirst and second frequencies and for connecting said counters to eachother, and a bistable switching element responsive to said first counterfor reversing the direction of counting of said first and secondcounters and for interchanging through said gate circuit means thefrequency sources to said counters.
 10. An apparatus as claimed in claim9 wherein said gate circuit means comprises a gate element for blockingthe resetting of the initial reading into the first counter prior to theexpiration of the first and second time periods.